Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite element methods

2016 ◽  
Vol 64 ◽  
pp. 205-221 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mostafa Abbaszadeh ◽  
Akbar Mohebbi
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Weak Form ◽  
Fractional Diffusion ◽  
Diffusion Wave ◽  
Element Free Galerkin ◽  
Element Free

A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Fengbin Liu ◽  
Qiang Wu ◽  
Yumin Cheng
Keyword(s):  
Large Deformation ◽  
Numerical Solutions ◽  
Weak Form ◽  
Weight Functions ◽  
Computational Accuracy ◽  
Lagrange Formulation ◽  
Element Free Galerkin ◽  
Penalty Factor ◽  
Element Free ◽  
Large Deformation Problems

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

scholarly journals Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Heng Cheng ◽  
Guodong Zheng
Keyword(s):  
Penalty Method ◽  
Weak Form ◽  
Singular Matrix ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Advection Diffusion ◽  
Computational Speed ◽  
The Difference ◽  
Element Free ◽  
Diffusion Problems

In this paper, the improved element-free Galerkin (IEFG) method is used for solving 3D advection-diffusion problems. The improved moving least-squares (IMLS) approximation is used to form the trial function, the penalty method is applied to introduce the essential boundary conditions, the Galerkin weak form and the difference method are used to obtain the final discretized equations, and then the formulae of the IEFG method for 3D advection-diffusion problems are presented. The error and the convergence are analyzed by numerical examples, and the numerical results show that the IEFG method not only has a higher computational speed but also can avoid singular matrix of the element-free Galerkin (EFG) method.

scholarly journals A GALERKIN FINITE ELEMENT METHOD TO SOLVE FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS

2013 ◽  
Vol 18 (2) ◽  
pp. 260-273 ◽  
Author(s):  
Alaattin Esen ◽  
Yusuf Ucar ◽  
Nuri Yagmurlu ◽  
Orkun Tasbozan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Galerkin Finite Element Method ◽  
Diffusion Wave ◽  
Galerkin Finite Element ◽  
Base Functions ◽  
Element Method

In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L 2 and L ∞ are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.

Coupled EFGM and F2LFEM for Fracture Analysis of Cracks

2009 ◽  
Author(s):  
K. N. Rajesh ◽  
B. N. Rao
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Consistency Condition ◽  
Shape Functions ◽  
Interface Elements ◽  
Element Free Galerkin ◽  
T Stress ◽  
Cracked Structures ◽  
As Stress ◽  
Element Free

This paper presents a coupling technique for integrating the element–free Galerkin method (EFGM) with fractal two-level finite element method (F2LFEM) for analyzing homogeneous, isotropic, and two dimensional linear–elastic cracked structures subjected to mixed–mode (modes I and II) loading conditions. F2LFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprises both the element–free Galerkin and the finite element shape functions, satisfies the consistency condition thus ensuring convergence of the proposed method. The proposed method combines the best features of EFGM and F2LFEM, in the sense that no structured mesh or special enriched basis functions are necessary and no post–processing (employing any path independent integrals) is needed to determine fracture parameters such as stress–intensity factors (SIFs) and T–stress. The numerical results show that SIFs and T–stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in this study. Also a parametric study is carried out to examine the effects of the similarity ratio, and the number of transformation terms on the quality of the numerical solutions.

A Coupled Finite Element-Element Free Galerkin Method for Liquefiable Soil-Structure Interaction Analysis Under Earthquake Loading

2009 ◽  
Author(s):  
Xiaowei Tang ◽  
Ying Jie ◽  
Maotian Luan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Soil Structure ◽  
Soil Structure Interaction ◽  
Element Free Galerkin Method ◽  
Structure Interaction ◽  
Element Free Galerkin ◽  
Liquefiable Soil ◽  
Element Free

This study presents a numerical method for the seismic behavior assessment of liquefiable soil-structure interaction. In the method, the element-free Galerkin method (EFGM) is applied to simulate the behavior of the liquefiable sandy soil which will take place large permanent deformation under earthquake loading. The finite element method (FEM) is used to describe the behavior of the structure. Then, the EFGM and FEM are related by contact elements. The cyclic elasto-plastic constitutive model and updated Lagrangian large-deformation formulation are jointly adopted to establish the governing equations in order to take account for both physical and geometrical nonlinearities. The shape function is established by moving least squares method while hexahedral background cells are used. The essential boundary conditions are treated with the help of the penalty method. The coupled method can avoid the volumetric locking in the numerical computations using finite element method when non-uniform deformations happen. In order to assess the effectiveness and accuracy of the current procedure, numerical simulation of caisson-type quay wall subjected to earthquake motion is conducted.

An Element-Free Galerkin-Finite Element Coupling Method for Elasto-Plastic Contact Problems

2005 ◽  
Vol 128 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Tianxiang Liu ◽  
Geng Liu ◽  
Q. Jane Wang
Keyword(s):  
Finite Element ◽  
Contact Problems ◽  
Elastic Cylinder ◽  
Coupling Method ◽  
Fe Method ◽  
Programming Technique ◽  
Galerkin Finite Element ◽  
Element Free Galerkin ◽  
Elasto Plasticity ◽  
Element Free

The element-free Galerkin-finite element (EFG-FE) coupling method, combined with the linear mathematical programming technique, is utilized to solve two-dimensional elasto-plastic contact problems. Two discretized models for an elastic cylinder contacting with a rigid plane are used to investigate the boundary effects in a contact problem when using the EFG-FE coupling method under symmetric conditions. The influences of the number of Gauss integration points and the size supporting the weight function in the meshless region on the contact pressure and stress distributions are studied and discussed by comparing the numerical results with the theoretical ones. Furthermore, the elasto-plastic contact problems of a smooth cylinder with a plane and a rough surface with a plane are analyzed by means of the EFG-FE method and different elasto-plasticity models.

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